Well, I probably do not know enough about the problem. Nevertheless, if you know the number of parts, then you know the approximate size of each part. You might want to avoid weird shapes of the parts. In that case, minimize the total of the boundary lengths.

It can be modefied superpixel generation algorithm (for example SLIC) or genetic algorithm.

This can be done geometrically to calculate the area of a section

Thanks all for your answers. I understand the geometric caculation and division of the area being

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Whereby n= number of sides of the polygon and x,y = vertices of the polygon

If you divide by m parts than each part should have area:

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However, my question would be through which steps, methods and using which criteria does one:

1) determine where the boundaries should of each sub part be? And, how does one optimize for example the minimum length of boundaries? (iteratively? mathematically?)

2) where the sub- parts should be (should one start at the top, or start at the bottom for example?)?

3) which logics would apply if areas should not be the same, but properties of the areas (such as sub-parcel values, average soil quality factors, compensation values, ecological values, etc.) should remain equal for all sub-parts.

4) which theories one can apply to divide land in a meaningful way?

basic mathematics / geometrics also at https://m.wikihow.com/Sample/Area-of-an-Irregular-Polygon

Thanks a lot for raising this interesting question, I am more than happy to follow this discussions on this.....may be some thoughts on - Presentation New Paradigm in Mapping: A Critique on Cartography and GIS

I believe that for one to resolve this given problem, attention needs to be drawn on the entire area to be subdivided. Taking x,y coordinate would be required from the existing road serving as condition one. Then a possible road one needs to be extended from the starting point in a manner that plots could be fixed without wasting land. That is condition must be given on shape that makes size of the road. Then other conditions follows to fix other plots

Numerical solution:

1 Create a regular grid of points within the domain.

2 Use k-means clustering for clustering the x- and y-coordinates of the points with k as the number of parts

3 Asign the cluster ID to the grid points

4 Use some geometric algorithm to construct a boundary around each set of points (e.g. convex hull)

Dear Dr. Walter = plot the shape on a millimetric paper, or try to find the coordinates of the parcel vertexes (latitude and longitudes in metric system )

. Using the formula of (( 2 Area = SUM ( Xn-1 * Yn ) –SUM ( Yn – Xn-1)) divided by 2 you will obtain the area of the parcel , then draw a line from any vertex draw a line to cut the circumference of the parcel at a point , say P with unknown coordinates (X .., Y ..) , make two equations, one for each of the required parts, but contain the un known point. Solve the problem to get the values of the coordinates of point P . this procedure is common in classical geometry .

I derived an algorithm to do exactly that in order to use it in a structural engineering program which finds ultimate resistances of arbitrary beam sections. I will not publish it here though since I am about to do a publication just for that by my-self. Just let me know where would you need that in order to see if we can publish any joint papers in the future.